Chapter 5: Interpreting Fractions In The Classroom

In the chapter, “Equal Sharing Problems and Children’s Strategies for Solving them” the authors recommend fractions be introduced to students through equal sharing problems that use countable quantities because they can be shared by people or other groupings. In other words, quantities can be split, cut, or divided. Additionally, equal sharing problems assist children to create “rich mental models “for fractions (p.10).

Math is all around us. Everywhere you go there is some sort of math involved consciously or subconsciously. Even though math is all around us, and everything we do involves math, I myself must say I dislike math. Research has shown there are many more people that dislike math compared to those who do like it. A survey done by a nonprofit organization named Change the Equation asked 1,000 middle school kids in 2010 whether they would prefer to eat broccoli or do one math problem, surprisingly more than half answered they would eat broccoli. Throughout the years, there have been many different strategies created on how to introduce and/or teach math to children.

In math we are supposed to learn or memorized plenty of formulas and compute them. In the video Why is Math Different Now by Dr. Raj Shah he talks about “how in math we give children standard algorithms, but we don’t understand where these numbers are coming from” (Shah). He provides an example by using two digit numbers multiple by two digit numbers. In this example he is saying how children do not understand the place values and where the extra zero is coming from, but in this new way of doing multiplication it shows the place values and where the zeros are coming from. This helps children understand the problem and not just getting the right answer like we have been doing in the past. The old method does not let students think freely or creatively. This approach helps children understand the number and just not worry about getting the right

Goal: At the end of the lesson the students will be able to evaluate twenty five fraction problems, and some of the fraction problems will include word problems

I would with one students on how to make equivalent fractions, She was very confused and did not know how. So I demonstrated the example that was written on the board. I wrote 3/6 and then wrote the division character by the numerator and denominator and then wrote 3. So then I said 3/3=1 and 6/3=2, then wrote 1/2. Then we tried to reduce 25/100, so I said, “What can you divide by 25 and 100.” She said 5 so she followed the example that I had written. So I said, what’s 100/5, she said, 20. So we knew the denominator was 20. Then I said whats 25/5, she said 5. So then I said the equivalent fraction is 5/20. She wrote done all that we had discussed above as we were finding the answer. I still think she was a little confused after, but it was time for discussion. For next time, I think I would try multiplying as another example, which I think could help the student see both. what I would have done was try multiplying instead of

Montana is working towards using effective strategies for comparing fractions. She identified that 2/4 and 4/8 were ‘both halves, therefore, the same’ (equivalent fractions); she used a

All of the previous work the students have done with the manipulatives and the visual aids should have given them a good foundation for writing fractions and seeing how they are represented with numbers and not just physical parts or fractions of a whole. There is a pattern between equivalent fractions that is based on counting by multiples. It can also be explained on knowing and using basic multiplication tables. To find an equivalent fraction is basic multiplication of both the numerator and the denominator by a number that is more than one or zero. Two is a very good base, low number to start with. Next is to explain to the students that with equivalent fraction problems you are looking for that missing number, that missing part that makes it complete.

For this game, adaptions can be made for students who struggle with thinking quickly when it comes to multiplication and dividions, with different possible selections of flash cards being made. For students who struggle with thinking quickly with multiplication, easier multiplications such as 2, 3, 5 and 10 times tables can be

Explain to students the mnemonic “Does McDonalds Sell Cheese Burgers?” will help them remember the steps for division

Learning about the long and tiresome process of transforming ordinary fractions into decimal fractions has made me realize how much I had taken for granted using calculator for the past decade. There are downsides to relying more on the calculator than relying on “old-fashioned” mind. “Patterns as Aids” becomes a problem when a student follows rules without understanding and calculates large numbers mentally using tricks but fails to understand the purpose of the processes or steps. Therefore it is better to understand less but thoroughly, than to be an expert in memorizing tricks and rules without any understanding. Principles must be taken apart, and each ingredient learned and taught individually. When something sounds hard or difficult, it usually means we did not break the problem into portions. Often I take for granted and overlooked simple aspects of math that I automatically perform. This book also mentions the importance of using word

The pre-assessment used to establish students' baseline knowledge and skills for this lesson was a comparing fractions pre-test. Students compared the following types of fraction comparisons: unit fractions, benchmark fractions, normal fractions, equivalent fractions, improper fraction vs. normal fractions, and improper vs. improper fractions. I have taken the information and used it to figure out which types of comparisons the students understand and using it to work on increasing the students' ability to include the other types. I use the information to accommodate what the students already know about the target. It showed me that students do not understand how to compare fractions, when they have a different denominator.

Part two of Ron Aharoni’s “Arithmetic for Parents” begins by introducing the topic of conveying abstractions. It is stated that in order to successfully convey abstractions to an individual, one must use concrete examples. When individuals learn ideas, they need to take small steps and work their way slowly—step-by-step—to the top. Aharoni maintains that teaching mathematical ideas follows the aforementioned principle. To begin learning, one must begin with what they know as familiar. The next topic covered explains the need for using diverse examples when teaching. For instance, Aharoni uses the concept of teaching children about what constitutes a dog. When explaining this concept, it is vital to let them know if you mean dogs in general or a particular

The first lesson observed shows Christie Kawalsky (Christie) at St. Albans East Primary School teaching fractions to a Year 3 class (Australian Institute for Teaching and School Leadership [AITSL] (Producer). (n.d.-a).

Upon observing a 6th grade math class I observed the teacher teaching the student’s about order of observation to evaluate algebraic expression. On the following day the teacher introduced the students into the concept of translating math phrases into numbers, variables, and operations. At the completion of my class observation I was able to administer a formative assessment on ratios. This paper will document what was observed during the ratio assessment.

Multiplicative thinking, fractions and decimals are important aspects of mathematics required for a deep conceptual understanding. The following portfolio will discuss the key ideas of each and the strategies to enable positive teaching. It will highlight certain difficulties and misconceptions that children face and discuss resources and activities to help alleviate these. It will also acknowledge the connections between the areas of mathematics and discuss the need for succinct teaching instead of an isolated approach.